Đáp án:

Giải thích các bước giải:

\(\begin{array}{*{20}{l}}
{\mathop {\lim }\limits_{x \to {\rm{\;}} - 1} \frac{{\sqrt[3]{x} + 1}}{{\sqrt {{x^2} + 3} {\rm{\;}} - 2}} = \mathop {\lim }\limits_{x \to {\rm{\;}} - 1} \frac{{\left( {\sqrt[3]{x} + 1} \right).\left( {\sqrt {{x^2} + 3} {\rm{\;}} + 2} \right)}}{{{x^2} + 3 - 4}}}\\
{ = \mathop {\lim }\limits_{x \to {\rm{\;}} - 1} \frac{{\left( {\sqrt[3]{x} + 1} \right).\left( {\sqrt {{x^2} + 3} {\rm{\;}} + 2} \right)}}{{\left( {x - 1} \right)\left( {\sqrt[3]{{{x^3}}} + 1} \right)}}}\\
{ = \mathop {\lim }\limits_{x \to {\rm{\;}} - 1} \frac{{\left( {\sqrt[3]{x} + 1} \right).\left( {\sqrt {{x^2} + 3} {\rm{\;}} + 2} \right)}}{{\left( {x - 1} \right)\left( {\sqrt[3]{x} + 1} \right)\left( {\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1} \right)}}}\\
{ = \mathop {\lim }\limits_{x \to {\rm{\;}} - 1} \frac{{\sqrt {{x^2} + 3} {\rm{\;}} + 2}}{{\left( {x - 1} \right)\left( {\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1} \right)}} = \frac{{ - 2}}{3}}
\end{array}\)